1,1,2,3,5,8,13,21,34

2025-09-14 阅读 64 评论 0

摘要：The given sequence is the Fibonacci sequence, where each number is the sum of the two preceding ones

The given sequence is the Fibonacci sequence, where each number is the sum of the two preceding ones, starting from 1 and 1. Here's the breakdown:

Pattern:

( F(n) = F(n-1) + F(n-2) ), with ( F(1) = 1 ) and ( F(2) = 1 ).

Sequence:

( 1, 1, 2, 3, 5, 8, 13, 21, 34, dots )

Next Terms:

After 34, the sequence continues as ( 55, 89, 144, dots ).

Key Properties:

The ratio of consecutive terms approaches the golden ratio (( phi approx 1.618 )). For example, ( frac{34}{21} approx 1.619 ).

Appears in nature (e.g., branching trees, flower petals) and mathematics (e.g., number theory, combinatorics).

This sequence is foundational in mathematics and has widespread applications in science, art, and computer algorithms.

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